Question: Simplify to lowest terms. $\dfrac{72}{45}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 72 and 45? $72 = 2\cdot2\cdot2\cdot3\cdot3$ $45 = 3\cdot3\cdot5$ $\mbox{GCD}(72, 45) = 3\cdot3 = 9$ $\dfrac{72}{45} = \dfrac{8 \cdot 9}{ 5\cdot 9}$ $\hphantom{\dfrac{72}{45}} = \dfrac{8}{5} \cdot \dfrac{9}{9}$ $\hphantom{\dfrac{72}{45}} = \dfrac{8}{5} \cdot 1$ $\hphantom{\dfrac{72}{45}} = \dfrac{8}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{72}{45}= \dfrac{3\cdot24}{3\cdot15}= \dfrac{3\cdot 3\cdot8}{3\cdot 3\cdot5}= \dfrac{8}{5}$